Our understanding of quantum materials is commonly based on precise determinations of their electronic spectrum by spectroscopic means, most notably angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy. Both require atomically clean and flat crystal surfaces, which are traditionally prepared by in situ mechanical cleaving in ultrahigh vacuum chambers. We present a new approach that addresses three main issues of the current state-of-the-art methods: (1) Cleaving is a highly stochastic and, thus, inefficient process; (2) fracture processes are governed by the bonds in a bulk crystal, and many materials and surfaces simply do not cleave; and (3) the location of the cleave is random, preventing data collection at specified regions of interest. Our new workflow is based on focused ion beam machining of micro-strain lenses, in which shape (rather than crystalline) anisotropy dictates the plane of cleavage, which can be placed at a specific target layer. As proof-of-principle, we show ARPES results from micro-cleaves of Sr₂RuO₄ along the ac plane and from two surface orientations of SrTiO₃, a notoriously difficult to cleave cubic perovskite.